Logarithm

Ok...here's an example

Let's suppose that we have

10^{log₁₀ 100}

Notice that log₁₀100    just evaluates to "2"

So we really have

10²  = 100       which was just the number that we were taking the log of in the exponent!!!

And since 10^10 was the number that we were taking the log of in the exponent, the answer just ends up being just..... 10^10

Check this question. http://web2.0calc.com/questions/logarithm_5

10^{log₁₀ (10^10)}

Whenever we have something like this...... a^log_ab   the answer is just "b"

So we have

10^{log₁₀(10^10)}

And the answer is just .....  10^10

But how does that work? could you do a step-by-step?